Question

Ken has made a selection of square jam sandwiches for a party, which he arranges in a single layer on the table in a perfect rectangle. Sarah has brought along the same number of square peanut butter sandwiches, which she puts out, also as a single layer, to form a border (one sandwich wide) around Ken’s rectangle. Given that all of the sandwiches are the same size and they are all used, how many sandwiches could each person possible have made?

Answer 1

Perimetre + 4 = area
Each person must have made 24

Answer 2

Each person possibly have made 24 or 30 sandwiches.

Explanation

Lets assume, there are 'm' number of sandwiches across the length and 'n' number of sandwiches across the width of rectangle.

So, the number of sandwiches for Ken $= m*n$

Now Sarah is making the border of the rectangle using same size sandwiches.

So, the number of sandwiches for Sarah $= m+n+m+n +4 = 2m+2n+4$ (As there will be 4 extra sandwiches at four corner of the border)

The question says that both Ken and Sarah is using same number of sandwiches. So, $2m+2n+4 = m*n$

This equation will be only satisfied if the values of 'm' and 'n' are either 6 and 4 or 10 and 3

If m=6 and n=4 , then each person have made (6×4)= 24 sandwiches

and if m=10 and n=3 , then each person have made (10×3)= 30 sandwiches